Improved solutions to the nonlinear one-dimensional Debye screening in plasmas with two temperatures

Abstract

Three new approximants to the solution of the one-dimensional nonlinear Debye screening potential have been obtained. The ions and electrons are in steady-state equilibrium situations with different temperatures. Therefore, the potential satisfies the nonlinear Poisson equation with a Boltzmann factor for both the electronic and ion densities. To obtain the approximants, the original equation has been written in a suitable compact way. The variables have been transformed in such a way that the two-point quasifractional approximation technique can be applied. The simplest approximant is almost as simple as the usual linear one, but it has an additional coefficient and it is more accurate. The other two approximants, more accurate than the simplest one, are exact for the limit of equal temperatures. All the approximants obtained here give better accuracy than the third-order approximation obtained previously by Clemente and Martín [J. Phys. Soc. Jpn. 61, 34 (1992)].